IDEAS home Printed from https://ideas.repec.org/p/cdf/wpaper/2019-3.html
   My bibliography  Save this paper

Nash vs. Coarse Correlation

Author

Listed:
  • Georgalos, Konstantinos

    (Department of Economics, Lancaster University Management School, Lancaster Universit)

  • Ray, Indrajit

    (Cardiff Business School)

  • Gupta, Sonali Sen

    (Department of Economics, Lancaster University Management School, Lancaster Universit)

Abstract

We run a laboratory experiment with a two-person game with unique pure Nash equilibrium which is also the solution of the iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes in this game (including the Nash equilibrium) with higher ex-ante expected payoff than the pure Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium as in Moulin and Vial, 1978), instead, they choose to play the game and then coordinate on the pure Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash equilibrium, the lottery is chosen by the individuals. The result is robust against variations like (i) a lottery choice for a pair of individuals, (ii) different payoffs in the game and (iii) the fixed-match between pairs.

Suggested Citation

  • Georgalos, Konstantinos & Ray, Indrajit & Gupta, Sonali Sen, 2019. "Nash vs. Coarse Correlation," Cardiff Economics Working Papers E2019/3, Cardiff University, Cardiff Business School, Economics Section.
    • Handle: RePEc:cdf:wpaper:2019/3
    as

    Download full text from publisher

    File URL: http://carbsecon.com/wp/E2019_3.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04, Department of Economics, University of Birmingham.
    3. Brandts Jordi & Macleod W. Bentley, 1995. "Equilibrium Selection in Experimental Games with Recommended Play," Games and Economic Behavior, Elsevier, vol. 11(1), pages 36-63, October.
    4. Ernst Fehr & Klaus M. Schmidt, 1999. "A Theory of Fairness, Competition, and Cooperation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 817-868.
    5. Jasmina Arifovic & George Evans & Olena Kostyshyna, 2013. "Are Sunspots Learnable? An Experimental Investigation in a Simple General-Equilibrium Model," Staff Working Papers 13-14, Bank of Canada.
    6. Giovanna Devetag & Andreas Ortmann, 2007. "When and why? A critical survey on coordination failure in the laboratory," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 331-344, September.
    7. Van Huyck, John B & Battalio, Raymond C & Beil, Richard O, 1990. "Tacit Coordination Games, Strategic Uncertainty, and Coordination Failure," American Economic Review, American Economic Association, vol. 80(1), pages 234-248, March.
    8. Ben Greiner, 2015. "Subject pool recruitment procedures: organizing experiments with ORSEE," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 1(1), pages 114-125, July.
    9. Alexander W. Cappelen & James Konow & Erik ?. S?rensen & Bertil Tungodden, 2013. "Just Luck: An Experimental Study of Risk-Taking and Fairness," American Economic Review, American Economic Association, vol. 103(4), pages 1398-1413, June.
    10. Cooper, Russell, et al, 1990. "Selection Criteria in Coordination Games: Some Experimental Results," American Economic Review, American Economic Association, vol. 80(1), pages 218-233, March.
    11. Timothy Cason & Tridib Sharma, 2007. "Recommended play and correlated equilibria: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(1), pages 11-27, October.
    12. Charness, Gary, 2000. "Self-Serving Cheap Talk: A Test Of Aumann's Conjecture," Games and Economic Behavior, Elsevier, vol. 33(2), pages 177-194, November.
    13. repec:cup:judgdm:v:5:y:2010:i:2:p:83-101 is not listed on IDEAS
    14. Harsanyi John C., 1995. "A New Theory of Equilibrium Selection for Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 10(2), pages 318-332, August.
    15. Russell Cooper & Douglas V. DeJong & Robert Forsythe & Thomas W. Ross, 1992. "Communication in Coordination Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 739-771.
    16. Barrett, Scott, 1994. "Self-Enforcing International Environmental Agreements," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 878-894, Supplemen.
    17. Russell Cooper & Douglas V. DeJong & Robert Forsythe & Thomas W. Ross, 1989. "Communication in the Battle of the Sexes Game: Some Experimental Results," RAND Journal of Economics, The RAND Corporation, vol. 20(4), pages 568-587, Winter.
    18. Michal Krawczyk, 2011. "A model of procedural and distributive fairness," Theory and Decision, Springer, vol. 70(1), pages 111-128, January.
    19. Camera, Gabriele & Casari, Marco & Bigoni, Maria, 2013. "Binding promises and cooperation among strangers," Economics Letters, Elsevier, vol. 118(3), pages 459-461.
    20. Van Huyck, John B. & Gillette, Ann B. & Battalio, Raymond C., 1992. "Credible assignments in coordination games," Games and Economic Behavior, Elsevier, vol. 4(4), pages 606-626, October.
    21. Arijit Mukherji & Kevin A. McCabe & David E. Runkle, 2000. "An experimental study of information and mixed-strategy play in the three-person matching-pennies game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 421-462.
    22. John Duffy & Ernest K. Lai & Wooyoung Lim, 2017. "Coordination via correlation: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 265-304, August.
    23. Seely, Beth & Van Huyck, John & Battalio, Raymond, 2005. "Credible assignments can improve efficiency in laboratory public goods games," Journal of Public Economics, Elsevier, vol. 89(8), pages 1437-1455, August.
    24. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    25. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-1668, December.
    26. Indrajit Ray & Sonali Gupta, 2013. "Coarse correlated equilibria in linear duopoly games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 541-562, May.
    27. Douglas W. Diamond & Philip H. Dybvig, 2000. "Bank runs, deposit insurance, and liquidity," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 24(Win), pages 14-23.
    28. McKelvey, Richard D & Page, Talbot, 1990. "Public and Private Information: An Experimental Study of Information Pooling," Econometrica, Econometric Society, vol. 58(6), pages 1321-1339, November.
    29. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    30. Moreno, Diego & Wooders, John, 1998. "An Experimental Study of Communication and Coordination in Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 47-76, July.
    31. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
    32. COOPER, R. & DEJONG, D.V. & FORSYTHE, R. & Tom Ross, 1989. "Communication In The Battle Of The Sexes Game," Carleton Industrial Organization Research Unit (CIORU) 89-03, Carleton University, Department of Economics.
    33. Cabrales, Antonio & Garcia-Fontes, Walter & Motta, Massimo, 2000. "Risk dominance selects the leader: An experimental analysis," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 137-162, January.
    34. Polemarchakis, Herakles M. & Ray, Indrajit, 2006. "Sunspots, correlation and competition," Games and Economic Behavior, Elsevier, vol. 56(1), pages 174-184, July.
    35. Trivikram Dokka Venkata Satyanaraya & Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2019. "Improving Abatement Levels and Welfare by Coarse Correlation in an Environmental Game," Working Papers 266042710, Lancaster University Management School, Economics Department.
    36. Crawford, Vincent, 1998. "A Survey of Experiments on Communication via Cheap Talk," Journal of Economic Theory, Elsevier, vol. 78(2), pages 286-298, February.
    37. Andreoni, James & Brown, Paul M. & Vesterlund, Lise, 2002. "What Makes an Allocation Fair? Some Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 40(1), pages 1-24, July.
    38. MOULIN, Hervé & VIAL, Jean-Philippe, 1978. "Strategically zero-sum games: the class of games whose completely mixed equilibria connot be improved upon," LIDAM Reprints CORE 359, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    39. Straub, Paul G., 1995. "Risk dominance and coordination failures in static games," The Quarterly Review of Economics and Finance, Elsevier, vol. 35(4), pages 339-363.
    40. Todd R. Kaplan & Bradley J. Ruffle, 2012. "Which Way to Cooperate," Economic Journal, Royal Economic Society, vol. 122(563), pages 1042-1068, September.
    41. Gary E Bolton & Jordi Brandts & Axel Ockenfels, 2005. "Fair Procedures: Evidence from Games Involving Lotteries," Economic Journal, Royal Economic Society, vol. 115(506), pages 1054-1076, October.
    42. Moulin, Herve & Ray, Indrajit & Sen Gupta, Sonali, 2014. "Improving Nash by coarse correlation," Journal of Economic Theory, Elsevier, vol. 150(C), pages 852-865.
    43. Marimon Ramon & Spear Stephen E. & Sunder Shyam, 1993. "Expectationally Driven Market Volatility: An Experimental Study," Journal of Economic Theory, Elsevier, vol. 61(1), pages 74-103, October.
    44. Stefan T. Trautmann & Gijs Kuilen, 2016. "Process fairness, outcome fairness, and dynamic consistency: Experimental evidence for risk and ambiguity," Journal of Risk and Uncertainty, Springer, vol. 53(2), pages 75-88, December.
    45. John Duffy & Nick Feltovich, 2010. "Correlated Equilibria, Good And Bad: An Experimental Study," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(3), pages 701-721, August.
    46. Costa-Gomes, Miguel A., 2002. "A Suggested Interpretation of Some Experimental Results on Preplay Communication," Journal of Economic Theory, Elsevier, vol. 104(1), pages 104-136, May.
    47. Forgo, Ferenc & Fulop, Janos & Prill, Maria, 2005. "Game theoretic models for climate change negotiations," European Journal of Operational Research, Elsevier, vol. 160(1), pages 252-267, January.
    48. Jasmina Arifovic & Janet Hua Jiang, 2014. "Do Sunspots Matter? Evidence from an Experimental Study of Bank Runs," Staff Working Papers 14-12, Bank of Canada.
    49. Regina M. Anctil & John Dickhaut & Chandra Kanodia & Brian Shapiro, 2004. "Information Transparency and Coordination Failure: Theory and Experiment," Journal of Accounting Research, Wiley Blackwell, vol. 42(2), pages 159-195, May.
    50. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04r, Department of Economics, University of Birmingham.
    51. John B. Van Huyck & Raymond C. Battalio & Richard O. Beil, 1991. "Strategic Uncertainty, Equilibrium Selection, and Coordination Failure in Average Opinion Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(3), pages 885-910.
    52. Gerard-Varet, L. A. & Moulin, H., 1978. "Correlation and duopoly," Journal of Economic Theory, Elsevier, vol. 19(1), pages 123-149, October.
    53. Frank Heinemann & Rosemarie Nagel & Peter Ockenfels, 2004. "The Theory of Global Games on Test: Experimental Analysis of Coordination Games with Public and Private Information," Econometrica, Econometric Society, vol. 72(5), pages 1583-1599, September.
    54. Stahl, Dale O., 2013. "An experimental test of the efficacy of a simple reputation mechanism to solve social dilemmas," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 116-124.
    55. Anbarcı, Nejat & Feltovich, Nick & Gürdal, Mehmet Y., 2018. "Payoff inequity reduces the effectiveness of correlated-equilibrium recommendations," European Economic Review, Elsevier, vol. 108(C), pages 172-190.
    56. Cabrales, Antonio & Drouvelis, Michalis & Gurguc, Zeynep & Ray, Indrajit, 2018. "Do we need to listen to all stakeholders?: communicating in a coordination game with private information," Cardiff Economics Working Papers E2018/23, Cardiff University, Cardiff Business School, Economics Section.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    2. Trivikram Dokka Venkata Satyanaraya & Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2020. "Equilibrium Design by Coarse Correlation in Quadratic Games," Working Papers 301895429, Lancaster University Management School, Economics Department.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    2. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04r, Department of Economics, University of Birmingham.
    3. Johne Bone & Michalis Drouvelis & Indrajit Ray, 2013. "Coordination in 2 x 2 Games by Following Recommendations from Correlated Equilibria," Discussion Papers 12-04, Department of Economics, University of Birmingham.
    4. Antonio Cabrales & Michalis Drouvelis & Zeynep Gurguy & Indrajit Ray, 2017. "Transparency is Overrated: Communicating in a Coordination Game with Private Information," CESifo Working Paper Series 6781, CESifo.
    5. Konstantinos Georgalos & Indrajit Ray & Sonali Sen Gupta, 2017. "Coarse correlation and coordination in a game," Working Papers 151235570, Lancaster University Management School, Economics Department.
    6. Cabrales, Antonio & Drouvelis, Michalis & Gurguc, Zeynep & Ray, Indrajit, 2018. "Do we need to listen to all stakeholders?: communicating in a coordination game with private information," Cardiff Economics Working Papers E2018/23, Cardiff University, Cardiff Business School, Economics Section.
    7. Verena Kurz & Andreas Orland & Kinga Posadzy, 2018. "Fairness versus efficiency: how procedural fairness concerns affect coordination," Experimental Economics, Springer;Economic Science Association, vol. 21(3), pages 601-626, September.
    8. John Duffy & Ernest K. Lai & Wooyoung Lim, 2017. "Coordination via correlation: an experimental study," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(2), pages 265-304, August.
    9. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    10. Arifovic, Jasmina & Jiang, Janet Hua, 2019. "Strategic uncertainty and the power of extrinsic signals– evidence from an experimental study of bank runs," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 1-17.
    11. Fehr, Dietmar & Heinemann, Frank & Llorente-Saguer, Aniol, 2019. "The power of sunspots: An experimental analysis," Journal of Monetary Economics, Elsevier, vol. 103(C), pages 123-136.
    12. Feldhaus, Christoph & Rockenbach, Bettina & Zeppenfeld, Christopher, 2020. "Inequality in minimum-effort coordination," Journal of Economic Behavior & Organization, Elsevier, vol. 177(C), pages 341-370.
    13. Siebert, Jan & Yang, Guanzhong, 2021. "Coordination problems triggered by sunspots in the laboratory," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 94(C).
    14. Feldhaus, Christoph & Rockenbach, Bettina & Zeppenfeld, Christopher, 2020. "Inequality in minimum-effort coordination," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224650, Verein für Socialpolitik / German Economic Association.
    15. Friedman, Daniel & Rabanal, Jean Paul & Rud, Olga A. & Zhao, Shuchen, 2022. "On the empirical relevance of correlated equilibrium," Journal of Economic Theory, Elsevier, vol. 205(C).
    16. Trivikram Dokka & Hervé Moulin & Indrajit Ray & Sonali SenGupta, 2023. "Equilibrium design in an n-player quadratic game," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 419-438, June.
    17. Giovanna Devetag & Andreas Ortmann, 2007. "When and why? A critical survey on coordination failure in the laboratory," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 331-344, September.
    18. López-Pérez, Raúl & Pintér, Ágnes & Kiss, Hubert J., 2015. "Does payoff equity facilitate coordination? A test of Schelling's conjecture," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 209-222.
    19. Trivikram Dokka Venkata Satyanaraya & Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2020. "Equilibrium Design by Coarse Correlation in Quadratic Games," Working Papers 301895429, Lancaster University Management School, Economics Department.
    20. Francisca Jiménez-Jiménez & Javier Rodero Cosano, 2021. "Experimental cheap talk games: strategic complementarity and coordination," Theory and Decision, Springer, vol. 91(2), pages 235-263, September.

    More about this item

    Keywords

    Correlation; Coordination; Lottery; Risk dominance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cdf:wpaper:2019/3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Yongdeng Xu (email available below). General contact details of provider: https://edirc.repec.org/data/ecscfuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.